Question

Determine the number and type of solutions for 5x^2 + 1x + 7 = 0.

1 Rational Double

2 Irrational

2 Rational

2 Complex

Answer 1

these are the answers given to do the mc

Answer 2

2 complex

Answer 3

2 complex

Answer 4

Possible intermediate steps:
5 x^2+x+7 = 0

Solve the quadratic equation by completing the square:

Divide both sides by 5:
x^2+x/5+7/5 = 0

Subtract 7/5 from both sides:
x^2+x/5 = -7/5

Add 1/100 to both sides:
x^2+x/5+1/100 = -139/100

Factor the left hand side:
(x+1/10)^2 = -139/100

Take the square root of both sides:
abs(x+1/10) = (i sqrt(139))/10

Eliminate the absolute value:
x+1/10 = -(i sqrt(139))/10 or x+1/10 = (i sqrt(139))/10

Subtract 1/10 from both sides:
x = -1/10 i (-i+sqrt(139)) or x+1/10 = (i sqrt(139))/10

Subtract 1/10 from both sides:
x = -1/10 i (-i+sqrt(139)) or x = 1/10 i (i+sqrt(139))

so both are of type , complex